Local-global compatibility for l = p , I

Thomas Barnet-Lamb[1]; Toby Gee[2]; David Geraghty[3]; Richard Taylor[4]

  • [1] Department of Mathematics, Brandeis University
  • [2] Department of Mathematics, Northwestern University
  • [3] Princeton University and Institute for Advanced Study
  • [4] Department of Mathematics, Harvard University

Annales de la faculté des sciences de Toulouse Mathématiques (2012)

  • Volume: 21, Issue: 1, page 57-92
  • ISSN: 0240-2963

Abstract

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We prove the compatibility of the local and global Langlands correspondences at places dividing l for the l -adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations of GL n over an imaginary CM field, under the assumption that the automorphic representations have Iwahori-fixed vectors at places dividing l and have Shin-regular weight.

How to cite

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Barnet-Lamb, Thomas, et al. "Local-global compatibility for $l=p$, I." Annales de la faculté des sciences de Toulouse Mathématiques 21.1 (2012): 57-92. <http://eudml.org/doc/251021>.

@article{Barnet2012,
abstract = {We prove the compatibility of the local and global Langlands correspondences at places dividing $l$ for the $l$-adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations of $\operatorname\{GL\}_n$ over an imaginary CM field, under the assumption that the automorphic representations have Iwahori-fixed vectors at places dividing $l$ and have Shin-regular weight.},
affiliation = {Department of Mathematics, Brandeis University; Department of Mathematics, Northwestern University; Princeton University and Institute for Advanced Study; Department of Mathematics, Harvard University},
author = {Barnet-Lamb, Thomas, Gee, Toby, Geraghty, David, Taylor, Richard},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Langlands correspondences; automorphic forms; Galois representations; local-global compatibility},
language = {eng},
month = {1},
number = {1},
pages = {57-92},
publisher = {Université Paul Sabatier, Toulouse},
title = {Local-global compatibility for $l=p$, I},
url = {http://eudml.org/doc/251021},
volume = {21},
year = {2012},
}

TY - JOUR
AU - Barnet-Lamb, Thomas
AU - Gee, Toby
AU - Geraghty, David
AU - Taylor, Richard
TI - Local-global compatibility for $l=p$, I
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2012/1//
PB - Université Paul Sabatier, Toulouse
VL - 21
IS - 1
SP - 57
EP - 92
AB - We prove the compatibility of the local and global Langlands correspondences at places dividing $l$ for the $l$-adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations of $\operatorname{GL}_n$ over an imaginary CM field, under the assumption that the automorphic representations have Iwahori-fixed vectors at places dividing $l$ and have Shin-regular weight.
LA - eng
KW - Langlands correspondences; automorphic forms; Galois representations; local-global compatibility
UR - http://eudml.org/doc/251021
ER -

References

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  2. Barnet-Lamb (T.), Gee (T.), Geraghty (D.), and Taylor (R.).— Local-global compatibility for l = p , II (2011). 
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  8. Harris (M.) and Taylor (R.).— The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151, Princeton University Press, Princeton, NJ, With an appendix by Vladimir G. Berkovich (2001). Zbl1036.11027MR1876802
  9. Katz (N. M.) and Messing (W.).— Some consequences of the Riemann hypothesis for varieties over finite fields, Invent. Math. 23, p. 73-77 (1974). Zbl0275.14011MR332791
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  11. Kottwitz (R. E.).— Points on some Shimura varieties over finite fields, J. Amer. Math. Soc. 5, no. 2, p. 373-444 (1992). Zbl0796.14014MR1124982
  12. Mantovan (E.).— On the cohomology of certain PEL-type Shimura varieties, Duke Math. J. 129, no. 3, p. 573-610 (2005). Zbl1112.11033MR2169874
  13. Sug Woo Shin.— Galois representations arising from some compact Shimura varieties, Annals of Math. (2) 173, no. 3, p. 1645-1741 (2011). Zbl1269.11053MR2800722
  14. Taylor (R.) and Yoshida (T.).— Compatibility of local and global Langlands correspondences, J. Amer. Math. Soc. 20, no. 2, p. 467-493 (electronic) (2007). Zbl1210.11118MR2276777

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